Theory question 102
Linear and Simultaneous Equations(a) In the simultaneous equations: px + qy = 5; qx + py = −10; p and q are constants. If x = 1 and y = 2 is solution of the equation, find p and q
(b) Solve (4r − 3)/(6r + 1) = (2r − 1)/(3r + 4)
Show the model answer
Model answer
(a) p + 2q = 5 and q + 2p = −10.
From the first, p = 5 − 2q; substitute: q + 10 − 4q = −10, so q = 20/3 and p = 5 − 40/3 = −25/3.
(b) (4r − 3)(3r + 4) = (2r − 1)(6r + 1): 12r2 + 7r − 12 = 12r2 − 4r − 1, so 11r = 11 and r = 1.
Explanation
Substitute the given x and y to get two equations in p and q.